A Colorado legal firm has begun legal action on behalf of a group of fans after Sunday's six-car US Grand Prix.
Client Larry Bowers and other ticket holders are seeking reimbursement, claiming they were defrauded by the race in which 14 cars failed to start.
Despite the controversy, Indianapolis Speedway spokesman Ron Green said many fans had bought tickets for next year.
"The renewals far outnumbered people who waited in line to talk about the chance of a refund," he said.
But Speedway president Joie Chitwood admitted Sunday's debacle, caused by a boycott over tyre safety issues, may have done irreparable damage to Formula One in the United States.
"This sets us back in all of our efforts and all of the gains we've made in introducing this sport to America," Chitwood said after the race.
Elsewhere, some bookmakers have refunded bets on the 14 drivers who did not compete in the race.
"As each driver took part in the warm-up lap, by definition each wager would have been a loss," said Alex Czajkowski, marketing director of the Sportsbook gambling website.
"Many of our players are race fans and don't need the added frustration this race has already cost."